You can almost always convince another person to expand their perspective. You can't usually convince them they were wrong, but that shouldn't be the point of the discussion. If you're disagreeing, the goal should be to understand why the other person thinks the way they do, and help them understand why you think what you do.
If you're not really interested in understanding the other person, then you can never truly "win" an argument, you can only make the other person feel foolish.
Additionally, remember that if you discover that your originally thought was wrong, you haven't lost the argument, you're much closer to having won it. You're leaving the argument more knowledgable than you were when you entered it, which has to be the ultimate goal.
